Brookings Papers on E Activity, 1: 1988 Second-Order Private Costs and First-Order Business Cycles. Mankiw and Akerlof and Yellen make a simple but important point. They study imperfectly competitive economies and show that the cost of nominal dities to price setters can be much smaller than the macroeconomic ffects. An example that illustrates the cost to price setters is a firm that initially sets its price at the profit-maximizing level but does not adjust after the money supply falls. We let m () denote the firms profits as a function of its price and let P be the firms predetermined price and P* its profit-maximizing price, which it would set if it adjusted. Using a Taylor expansion, we can approximate the firms profit loss from not (1)丌(P*)-丌(P)≈丌(P)P*-P)-丌"(P*)(P*-P)2 But since P* maximizes profits, '(*)is zero. Thus the profit loss from nonadjustment is second order-that is, proportional to the square of (P*-P). As long as the predetermined price is close to the profit- maximizing price, the cost of price rigidity to the firm is small But rigidity can have first-order macroeconomic effects. An increase in nominal money with nominal prices fixed leads to a first-order increase in real aggregate demand, and hence in real output. For example, if the aggregate demand curve is simply y= M/P, rigid prices imply a change in output proportional to the change in money The effect on social welfare is also first order, as follows from the assumption of imperfect competition. Under imperfect competition, the profit-maximizing price is socially suboptimal. The price is too high and output is too low. Thus at P* the first derivative of welfare with respect to the firms price is negative: welfare would rise if the price fell below P*. Nonadjustment to a fall in money implies P greater than P*, given the negative first derivative of welfare, the welfare loss is first order. Because the cost of rigidity to a price setter is second order while the macroeconomic effects are first order, the latter can be much large This finding resolves the puzzle of why price setters refuse to incur the mall costs of reducing the business cycle through more flexible prices Despite the large macroeconomic effects, the private itives are Aggregate Demand Externalities. blanchard and Kiyotaki provide an important interpretation of the result in Mankiw and Akerlof-Yellen: